22. x*(5sinx - 3cosx)

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Solution

Let the given function be,

f( x )= x 4 ( 5sinx−3cosx )

Differentiate the function with respect to x,

f ′ ( x )=( 5sinx−3cosx ) d dx ( x 4 )+ x 4 d dx ( 5sinx−3cosx ) =( 5sinx−3cosx )( 4 x 3 )+ x 4 [ 5 d dx sinx−3 d dx cosx ] =( 5sinx−3cosx )4 x 3 + x 4 [ 5( cosx )+3sinx ] = x 3 [ 5xcosx+3xsinx+20sinx−12cosx ]

Therefore, the derivative of the function is x 3 [ 5xcosx+3xsinx+20sinx−12cosx ].

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